664 research outputs found
Migration of Earth-size planets in 3D radiative discs
In this paper, we address the migration of small mass planets in 3D radiative
disks. Indeed, migration of small planets is known to be too fast inwards in
locally isothermal conditions. However, thermal effects could reverse its
direction, potentially saving planets in the inner, optically thick parts of
the protoplanetary disc. This effect has been seen for masses larger than 5
Earth masses, but the minimum mass for this to happen has never been probed
numerically, although it is of crucial importance for planet formation
scenarios. We have extended the hydro-dynamical code FARGO to 3D, with thermal
diffusion. With this code, we perform simulations of embedded planets down to 2
Earth masses. For a set of discs parameters for which outward migration has
been shown in the range of Earth masses, we find that the transition
to inward migration occurs for masses in the range Earth masses. The
transition appears to be due to an unexpected phenomenon: the formation of an
asymmetric cold and dense finger of gas driven by circulation and libration
streamlines. We recover this phenomenon in 2D simulations where we control the
cooling effects of the gas through a simple modeling of the energy equation.Comment: 17 pages, 20 figures, accepted. MNRAS, 201
Entanglement Entropy in Quantum Mechanics: An Algebraic Approach
An algebraic approach to the study of entanglement entropy of quantum systems
is reviewed. Starting with a state on a -algebra, one can construct a
density operator describing the state in the GNS representation state.
Applications of this approach to the study of entanglement measures for systems
of identical particles are outlined. The ambiguities in the definition of
entropy within this approach are then related to the action of unitaries in the
commutant of the representation and their relation to modular theory explained.Comment: To be published in "Particles, Fields and Topology: Celebrating A.P.
Balachandran", a Festschrift volume for A.P. Balachandra
Meridional circulation of gas into gaps opened by giant planets in three-dimensional low-viscosity disks
We examine the gas circulation near a gap opened by a giant planet in a
protoplanetary disk. We show with high resolution 3D simulations that the gas
flows into the gap at high altitude over the mid-plane, at a rate dependent on
viscosity. We explain this observation with a simple conceptual model. From
this model we derive an estimate of the amount of gas flowing into a gap opened
by a planet with Hill radius comparable to the scale-height of a layered disk
(i. e. a disk with viscous upper layer and inviscid midplane). Our estimate
agrees with modern MRI simulations(Gressel et al., 2013). We conclude that gap
opening in a layered disk can not slow down significantly the runaway gas
accretion of Saturn to Jupiter-mass planets.Comment: in press as a Note in Icaru
- …